This invention relates in general to exercise equipment and in particular to dumbbells for use while exercising. In the applicant's previous teachings, there is disclosed an attachment which can be supported by a pair of vertical support columns commonly found in a standard weight-lifting bench. Used to support at least one dumbbell, this attachment works well with vertical support columns which are spaced apart from each other by a distance which matches the fixed span of the attachment. Needless to say, it does not fit all benches. Morever, the vertical mounting legs in this prior art attachment are situated rearwardly of its dumbbell holders as well as of the center of gravity of any dumbbell weights resting therein, thus generally limiting the use of the attachment to situations in which it can be mounted upon vertical support columns secured to a bench rather than upon free-standing columns.